Complex waves

I have learnt that with a musical instrument you set up standing waves of the fundamental frequency as well as other harmonics which cause the specific "quality" of the sound - my question is why do you produce different harmonics and not just the fundamental frequency? When you pluck a string or blow an air column why do you not just produce one wave? eg - the fundamental frequency?

if you look at any musical instrument out there, you will notice that all of them have some for of resonant cavity. For stringed instruments like violins and guitars and pianos, this is the body of the instrument. For wind instruments, this is the tube form of the instrument.

The standing wave vibrations you produce at the source (reed, string, whistle) are transmitted to the body which resonate at their particular frequencies. this is where many of the subharmonics that produce the tones and depth characteristic of different instruments come from.

The harmonics produced depend on the shape, material and construction of the resonant cavity.

I think one easy way of visualizing it is as follow. Take a guitar for instance, you pluck it by quickly displacing and releasing the string. Now the shape of the displaced string will have certain overlap with the fundamental vibrating mode, so some energy goes into this mode, and the same goes for higher order modes as well. So a large family of modes is excited by plucking.
However, you can also selectively excite a smaller family of modes as well, this is how artificial harmonic works in guitar and violin. For example by gently touching the middle point of a guitar/violin string when you pluck, you essentially introduce a node to that point by restraining it from vibrating. In this case only those vibrating modes with a node at the middle of the string will get excited.